Question

Geoffrey is evaluating the expression StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript 5 Baseline (2 squared) EndFraction as shown below. StartFraction (negative 3) cubed (2 Superscript 6 Baseline) Over (Negative 3) Superscript 5 Baseline (2 squared) EndFraction = StartFraction (2) Superscript a Baseline Over (negative 3) Superscript b Baseline EndFraction = StartFraction c Over d EndFraction What are the values of a, b, c, and d? a = 4, b = 2, c = 16, d = 9 a = 4, b = negative 2, c = 16, d = 9 a = 8, b = 8, c = 256, d = 6,561 a = 8, b = 8, c = 256, d = negative 6,561

Answer 1

The mathematical expression does not seem clear but I have made an attempt to make sense of what is implied.

Answer:

a = 4, b = 2, c = 16, d = 9

Step-by-step explanation:

$\dfrac{(-3)^3(2^6)}{(-3)^5(2^2)} = \dfrac{(2)^a}{(-3)^b} = \dfrac{c}{d}$

Solving the first part of the question by indices,

$\dfrac{(-3)^3(2^6)}{(-3)^5(2^2)} = (-3)^{3-5}(2)^{6-2} = (-3)^{-2}(2)^{4} = \dfrac{(2)^4}{(-3)^2}$

Comparing the rightmost term with the second term in the question,

a = 4, b = 2

Solving on,

$\dfrac{(2)^4}{(-3)^2} = \dfrac{(2)\times(2)\times(2)\times(2)}{(-3)\times(-3)} = \dfrac{16}{9}$

Comparing with the final term in the question,

c = 16 and d = 9

Therefore,

a = 4, b = 2, c = 16, d = 9

Answer 2

Answer:

It is A.) a=4 b=2 c=16 d=9

Step-by-step explanation:

I got a 100 on the test